A New Way to Analyze Paired Comparisons

The importance of “paired comparisons,” whether ordinal or cardinal, has motivated the creation of several methodological approaches; missing, however, is a common way to compare the various techniques. To do so, an approach developed here creates a coordinate system for the “data space.” The coordinates capture which data aspects satisfy a strong cardinal transitivity condition and which ones represent “noise;” i.e., this second component consists of highly cyclic aspects that are formed by the data. The data coordinate system is illustrated by analyzing a new paired comparison rule, by comparing behaviors of selective rules, and by answering concerns about the Analytic Hierarchy Process (AHP) (such as how to select an “appropriate” consistent data term for a non-consistent one). An elementary (and quick) way to obtain AHP weights is introduced.